CN109241613B - Method for determining cutter root trimming parameters of spiral bevel gear - Google Patents
Method for determining cutter root trimming parameters of spiral bevel gear Download PDFInfo
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- CN109241613B CN109241613B CN201811013117.8A CN201811013117A CN109241613B CN 109241613 B CN109241613 B CN 109241613B CN 201811013117 A CN201811013117 A CN 201811013117A CN 109241613 B CN109241613 B CN 109241613B
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Abstract
The invention discloses a method for determining the root trimming parameters of a cutter of a spiral bevel gear, which comprises the following steps: (1) determining the position of the root trimming effect range on the tooth surface of the mating gear; (2) determining the position of the back-off effect range on the tooth surface of the back-off gear; (3) determining the position of the root trimming effect range corresponding to the processing cutter of the gear to be trimmed; (4) and determining parameters of the root-trimming proud curve on the cutter. The problem of among the prior art confirm the process of cutter root-trimming proud parameter need try repeatedly, consume time and complex operation is solved. The invention can determine the parameters of the cutter root-trimming protruding head according to the parameters of the top of the matched gear teeth meshed with the root-trimming part of the gear to be root-trimmed, can directly calculate the result of the parameters of the cutter root-trimming protruding head, does not need to try repeatedly, and can improve the problems of tooth surface edge contact and stress concentration.
Description
Technical Field
The invention belongs to the technical field of spiral bevel gears, and particularly relates to a method for determining a cutter root trimming parameter of a spiral bevel gear.
Background
In the actual transmission process, the spatial relative position of the spiral bevel gear pair can not be at the standard installation position, because the gear, the gear shaft, the bearing, the casing and the like can deform under the condition of load, the true spatial position of the gear shaft can be staggered, and because of manufacturing errors, assembly errors, the relative position relation of the tooth surface is inconsistent with the state of theoretical design due to the tooth surface deformation and other reasons, the actual contact spot of the gear pair can deviate to other positions from the preset position, edge contact occurs, stress concentration is caused, gear meshing is not stable, gear vibration and squeal are caused, the gear strength is reduced, and further the tooth breakage phenomenon is caused.
In order to avoid edge contact and stress concentration, the tooth surfaces of the arc-tooth bevel gears need to be trimmed, and the tooth root parts of the gears are subjected to proper material reduction treatment relative to the original theoretical profile. The method is to add a root-trimming protruding head on the cutter outline, aiming at trimming a trimming area along the tooth width direction near the tooth root part, so as to remove more material at the tooth root part.
The parameters of the cutter root-trimming protruding head determine the tooth surface trimming amount, and proper selection is needed. The root trimming amount is too small, so that the effect of improving edge contact is not achieved; too much root trimming causes too much damage to the tooth flanks, which weakens the strength of the gear teeth. Because it is difficult to directly determine the range of the root of the spiral bevel gear, the existing method for determining the parameters of the root and the protruding head of the cutter is to give the parameters of the root and the protruding head of the cutter, then calculate the tooth surface data of the tooth to be root-removed, carry out TCA analysis on the gear pair after root removal, judge whether the meshing characteristics of the gear pair meet the requirements, if not, the parameters of the root and the protruding head of the cutter need to be modified, and finally determine the reasonable parameters of the root and the protruding head of the cutter through repeated attempts.
Disclosure of Invention
The invention aims to provide a method for determining the cutter root trimming parameters of a spiral bevel gear, which solves the problems that the process of determining the cutter root trimming protruding head parameters in the prior art needs to be repeatedly tried, the time is consumed and the operation is complicated. The invention can determine the parameters of the cutter root-trimming protruding head according to the parameters of the top of the matched gear teeth meshed with the root-trimming part of the gear to be root-trimmed, can directly calculate the result of the parameters of the cutter root-trimming protruding head, does not need to try repeatedly, and can improve the problems of tooth surface edge contact and stress concentration.
In order to achieve the purpose, the invention adopts the following technical scheme:
the invention provides a method for determining the root trimming parameters of a cutter of a spiral bevel gear, which comprises the following steps:
step (1) determining root pruning effectRange at the position of the mating gear tooth faces: the end point of the range of the root trimming effect on the tooth surfaces of the mating gears is
Point, determine
Coordinates of points in the rotated projection section
The starting point of the range of the root trimming effect on the tooth surfaces of the mating gears is
Point, determine
Coordinates of points in the rotated projection section
According to
Finding the end point of the root trimming effect range of the tooth surfaces of the mating gears
Position vector of
According to
Finding the initial point of the root trimming effect range of the tooth surfaces of the mating gears
Position vector of
Step (2) determining that the scope of the root pruning effect is within the range of the root pruning effectThe position of the tooth surface of the root gear: according to the meshing relation of the mating gear and the gear to be trimmed, the position vector of the tooth surface of the mating gear
Find and
on the tooth surface of the point-meshed gear to be relieved
Position vector of point
From position vectors of mating gear flanks
Find and
on the tooth surface of the point-meshed gear to be relieved
Position vector of point
Step (3), determining the position of the root trimming effect range corresponding to the machining cutter of the gear to be trimmed: the position vector on the tooth surface of the gear to be processed and the root is solved through coordinate conversion
Is/are as follows
Corresponding to the position vector in the tool coordinate system
And a position vector of
Is/are as follows
Corresponding to the position vector in the tool coordinate system
Further obtaining the tooth surface of the machined gear to be root-removed
Dot sum
The point corresponds to the axial height on the cutter;
step (4), determining parameters of the root trimming proud curve on the cutter: on the tooth surface of the gear to be root according to the machining
Dot sum
And (3) corresponding to the axial height of the cutter, and solving the parameters of the root-trimming proud curve on the cutter by using the geometric relation and the designed modification amount.
Furthermore, the invention is characterized in that:
in the step (1), on the tooth surface of the mating gear, the tooth crest boundary point of the mating gear is the end point of the root trimming effect range
The height range of the root trimming amount acting in the tooth height direction is
From
Point down
The height position is used as the starting point of the root trimming effect range
In the step (1), the root trimming effect range of the concave surface of the mating gear is determined from the tooth top of the small end, and the root trimming effect range of the convex surface of the mating gear is determined from the tooth top of the large end.
In step (1), the coordinates in the section of the rotational projection are two-dimensional coordinates where one point on the tooth surface corresponds to the section of the gear shaft.
In the step (3), processing
Dot sum
The axial height of the point corresponding to the cutter is as follows: from the top surface of the tool to the tool profile
The height of the point in the direction of the tool axis, and the machining from the tool top surface onto the tool profile
The height of the point of points in the direction of the tool axis.
In step (4), the designed modification amount is used for processing on the tool profile
The normal distance of the point with respect to the original tool profile.
The root trimming effect range refers to a range in which a root trimming area influences a tooth surface meshing area of the gear pair; for the tooth surface of the tooth to be trimmed, the trimming effect range refers to the position of the tooth root part which is additionally removed with material by the trimming protruding head of the cutter relative to the tooth surface which is not trimmed; for mating gear tooth surfaces, the back-off effect range refers to the location of intermeshing with the back-off region of the back-off gear.
The invention can only carry out root trimming on the large wheel of the arc-tooth bevel gear pair; or only the small wheel of the arc-tooth bevel gear pair is trimmed; or simultaneously trimming the large wheel and the small wheel of the arc-tooth bevel gear pair.
Compared with the prior art, the invention has the following beneficial technical effects:
the invention provides a method for determining the parameters of the cutter root trimming and the protruding head of a spiral bevel gear, which can determine the parameters of the cutter root trimming and the protruding head of the cutter according to the parameters of the top of the matched gear teeth meshed with the root trimming part of a gear to be trimmed, can directly calculate the results of the parameters of the cutter root trimming and the protruding head of the cutter, does not need repeated try, saves time and is easy to operate. The method can conveniently determine the proper parameters of the cutter root-trimming protruding head curve, improve the problems of tooth surface edge contact and stress concentration, and is suitable for cutter root-trimming protruding head curves of different styles.
Drawings
Fig. 1 is a schematic view of a rotation projection section of a mating gear.
FIG. 2 is a sectional view of a cutter shaft for a small wheel arc type root cutting.
FIG. 3 shows contact spots on the convex surface of the large wheel before the small wheel is gouged.
FIG. 4 shows the contact spots on the convex surface of the large wheel after the small wheel has been cut.
Detailed Description
The invention is described in further detail below with reference to the accompanying drawings:
the invention provides a method for determining the root trimming parameters of a cutter of a spiral bevel gear, which comprises the following steps:
step (1), determining the position of the root trimming effect range on the tooth surface of the mating gear: the end point of the range of the root trimming effect on the tooth surfaces of the mating gears is
Point, determine
Coordinates of points in the rotated projection section
The starting point of the range of the root trimming effect on the tooth surfaces of the mating gears is
Point, determine
Coordinates of points in the rotated projection section
According to
Finding the end point of the root trimming effect range of the tooth surfaces of the mating gears
Position vector of
According to
Finding the initial point of the root trimming effect range of the tooth surfaces of the mating gears
Position vector of
Here, as shown in fig. 1, on the mating gear tooth surface, the mating gear tooth crest boundary point is the root effect range end point
The height range of the root trimming amount acting in the tooth height direction is
From
Point down
The height position is used as the starting point of the root trimming effect range
Here, the range of the root-modifying effect of the concave surface of the mating gear is determined from the tip of the small end tooth, and the range of the root-modifying effect of the convex surface of the mating gear is determined from the tip of the large end tooth.
Here, the coordinates in the rotational projection section refer to two-dimensional coordinates in which a point on the tooth surface corresponds to the gear shaft section.
Step (2), determining the position of the root trimming effect range on the tooth surface of the gear to be root trimmed: according to the meshing relation of the mating gear and the gear to be trimmed, the position vector of the tooth surface of the mating gear
Find and
on the tooth surface of the point-meshed gear to be relieved
Position vector of point
From position vectors of mating gear flanks
Find and
on the tooth surface of the point-meshed gear to be relieved
Position vector of point
Step (3), determining the position of the root trimming effect range corresponding to the machining cutter of the gear to be trimmed: the position vector on the tooth surface of the gear to be processed and the root is solved through coordinate conversion
Is/are as follows
Corresponding to the position vector in the tool coordinate system
And a position vector of
Is/are as follows
Corresponding to the position vector in the tool coordinate system
Further obtaining the tooth surface of the machined gear to be root-removed
Dot sum
The point corresponds to the axial height on the tool.
In addition, the processing is performed
Dot sum
The axial height of the point corresponding to the cutter is as follows: from the top surface of the tool to the tool profile
Of dotsHeight of point along tool axis, and machining from tool top surface to tool profile
The height of the point of points in the direction of the tool axis.
Step (4), determining parameters of the root trimming proud curve on the cutter: on the tooth surface of the gear to be root according to the machining
Dot sum
And (3) corresponding to the axial height of the cutter, and solving the parameters of the root-trimming proud curve on the cutter by using the geometric relation and the designed modification amount.
The designed modification amounts are used for machining on the tool contour
The normal distance of the point with respect to the original tool profile, this amount being given according to the actual operating conditions.
In the invention, the root trimming effect range refers to a range in which a root trimming area influences a tooth surface meshing area of a gear pair; for the tooth surface of the tooth to be trimmed, the trimming effect range refers to the position of the tooth root part which is additionally removed with material by the trimming protruding head of the cutter relative to the tooth surface which is not trimmed; for mating gear tooth surfaces, the back-off effect range refers to the location of intermeshing with the back-off region of the back-off gear.
The invention can only carry out root trimming on the large wheel of the arc-tooth bevel gear pair; or only the small wheel of the arc-tooth bevel gear pair can be trimmed; the root of the large wheel and the small wheel of the arc-tooth bevel gear pair can be repaired at the same time.
The invention is illustrated below with reference to specific examples:
example (b):
for a pair of arc-tooth bevel gear pairs used on a rear axle of a passenger car, roots of the small wheel are trimmed, parameters of a root trimming protruding head curve of a small wheel cutter are solved, the root trimming protruding head adopts an arc type, and the root trimming of a concave surface of the small wheel is taken as an example.
The basic parameters of the gear pair are as in table 1:
TABLE 1 basic parameters of the gear pairs
The specific implementation is as follows:
(1) determining the position of the root trimming effect range on the tooth surface of the large wheel:
although the root of the small gear is modified, it is difficult to determine the root modification range directly at the root of the small gear, and it is convenient to determine the range of the modification effect from the top of the corresponding large gear, so the initial point of the root modification effect range is determined first
End point of point and root effect range
Coordinates of points in the section of the large wheel rotating projection
The convex surface of the big wheel is engaged with the concave surface of the small wheel, and the contact trace trend of the convex surface of the big wheel is from the big end tooth crest to the small end tooth root of the big wheel, so the root trimming effect range of the convex surface of the big wheel is determined from the big end tooth crest. In FIG. 1, the top boundary point of the bull wheel is the end point of the root trimming effect range
The height range of the point and the modification quantity acting in the tooth height direction is
So as to get from
Point down
The height position is used as the starting point of the root trimming effect range
And (4) point. Then determining
Dot sum
The rotational projection coordinates of the points are respectively
And
from the rotational projection coordinates
Dot sum
Position vector corresponding to tooth surface of large wheel
And
(2) determining the position of the root trimming effect range on the small wheel tooth surface:
according to the meshing relation of the big wheel and the small wheel, the position vector of the surface point of the big wheel is determined
And
respectively finding the tooth surface points of the small wheel engaged with the small wheel
And
position vector of
And
(3) determining the position corresponding to the small wheel cutter:
since the processing parameters of the small wheel are determined, the position vector on the tooth surface of the small wheel can be solved by coordinate conversion
And
the point of interest corresponds to a position vector in the tool coordinate system
And
thereby obtaining the surface of the tooth of the small wheel
And
axial height h of point corresponding to cutterEAnd hBThe correspondences are points E and B on the tool profile, as shown in fig. 2. The corresponding relation is a point
-points
Point E (h)E) Sum point
-points
Point B (h)B)”。
(4) Determining parameters of a root trimming circular arc on a cutter:
machining
The point B of the point is tangent to the original straight line blade, and the processing is carried out
The normal root trimming amount of the point E relative to the original straight line edge is
Namely, the designed modification amount, the value is given according to the actual requirement, the following formula can be determined through the geometrical relation, and the value meeting the following formula can be obtained through iteration.
The radius rho of the arc BC section can be obtained by the following formularThe entire edge profile of the small wheel cutter can then be expressed.
Finally determined height h of point B on the root trimming circular arc of the external edge of the small wheel cutterB5.953mm, the radius of the root trimming circular arc is 58.681 mm.
It should be noted that, in fig. 2, the AB segment is a straight line blade for machining the tooth surface of the small wheel, the BC segment is an added root trimming arc protruding head for removing more material from the root of the small wheel, the CD segment is a nose arc for machining the transition curved surface, in fig. 2, for illustrating that the BC segment is drawn more exaggeratedly, the actual root trimming amount is in the micrometer level, the tooth surface is micro-adjusted, the height and thickness of the protruding head part are not as large as those in fig. 2, αcPressure of the blade being the outer edge of the toolAn angle; o isrIs the center of the arc BC, ρrIs the radius of arc BC; the point E is a point on the arc BC, and the point EF is the normal root trimming amount of the point E relative to the original straight line blade; h isBIs the distance along the tool axis from point B to the top surface of the tool, hEIs the distance along the tool axis from point E to the top surface of the tool.
Fig. 3 and 4 are comparisons of contact spots on the convex surface of the large wheel before and after the small wheel is pedicured. It can be seen that before the small wheel is trimmed, the contact spot is connected with the tooth top boundary of the large wheel; after the small wheel is trimmed, the contact spots are completely separated from the top boundary of the large wheel tooth, the whole contact spots are all in the side frame of the tooth surface, and the edge contact of the tooth top of the large wheel is avoided, so that the method is proved to be effective.
Claims (7)
1. A method for determining the root trimming parameter of a cutter of a spiral bevel gear is characterized by comprising the following steps:
step (1), determining the position of the root trimming effect range on the tooth surface of the mating gear: the end point of the range of the root trimming effect on the tooth surfaces of the mating gears is
Point, determine
Coordinates of points in the rotated projection section
The starting point of the range of the root trimming effect on the tooth surfaces of the mating gears is
Point, determine
Coordinates of points in the rotated projection section
According to
Finding the end point of the root trimming effect range of the tooth surfaces of the mating gears
Position vector of
According to
Finding the initial point of the root trimming effect range of the tooth surfaces of the mating gears
Position vector of
Step (2), determining the position of the root trimming effect range on the tooth surface of the gear to be root trimmed: according to the meshing relation of the mating gear and the gear to be trimmed, the position vector of the tooth surface of the mating gear
Find and
on the tooth surface of the point-meshed gear to be relieved
Position vector r of points1 PFrom position vectors of tooth surfaces of mating gears
Find and
on the tooth surface of the point-meshed gear to be relieved
Position vector of point
Step (3), determining the position of the root trimming effect range corresponding to the machining cutter of the gear to be trimmed: solving the position vector r on the tooth surface of the machined root gear through coordinate conversion1 PIs/are as follows
Corresponding to the position vector in the tool coordinate system
And a position vector of
Is/are as follows
Corresponding to the position vector r in the tool coordinate system2 cFurther obtaining the tooth surface of the gear to be machined and repaired
Dot sum
The point corresponds to the axial height on the cutter;
step (4), determining parameters of the root trimming proud curve on the cutter: on the tooth surface of the gear to be root according to the machining
Dot sum
Corresponding to the axial height of the point on the cutter, and solving the parameters of the root-trimming proud curve on the cutter by using the geometric relation and the designed modification amount;
wherein the flank of the tooth of the gear to be relieved is machined
Dot sum
The axial height of the point corresponding to the cutter is as follows: from the top surface of the tool to the tool profile
The height of the point in the direction of the tool axis, and the machining from the tool top surface onto the tool profile
The height of the point of points in the direction of the tool axis.
2. The method for determining the tool back-off parameters for spiral bevel gears as defined in claim 1 wherein in step (1), the tooth crest boundary point of the mating gears on the tooth flanks of the mating gears is the end point of the back-off effect range
The height range of the root trimming amount acting in the tooth height direction is
From
Point down
The height position is used as the starting point of the root trimming effect range
3. The method for determining the tool back-chipping parameter of a spiral bevel gear according to claim 1, wherein in step (1), the range of the back-chipping effect of the concave surface of the mating gear is determined from the small-end crest and the range of the back-chipping effect of the convex surface of the mating gear is determined from the large-end crest.
4. The method for determining the tool back-off parameters for spiral bevel gears as claimed in claim 1, wherein in step (1), the coordinates in the cross-section of the rotational projection are two-dimensional coordinates of a point on the tooth surface corresponding to the cross-section of the gear shaft.
5. The method for determining the tool back-off parameters for spiral bevel gears as set forth in claim 1, wherein the designed back-off amount in step (4) is defined as the amount of back-off that is applied to the tool profile for machining
The normal distance of the point with respect to the original tool profile.
6. The method for determining the cutter back-off parameters of spiral bevel gears according to claim 1, wherein the back-off effect range is a range in which a back-off region affects a tooth surface meshing region of a gear pair; for the tooth surface of the tooth to be trimmed, the trimming effect range refers to the position of the tooth root part which is additionally removed with material by the trimming protruding head of the cutter relative to the tooth surface which is not trimmed; for mating gear tooth surfaces, the back-off effect range refers to the location of intermeshing with the back-off region of the back-off gear.
7. The method for determining the tool chipping parameter of the spiral bevel gear according to claim 1, wherein only the large gear of the spiral bevel gear pair is chipped; or only the small wheel of the arc-tooth bevel gear pair is trimmed; or simultaneously trimming the large wheel and the small wheel of the arc-tooth bevel gear pair.
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| CN109732153B (en) * | 2019-01-08 | 2021-01-05 | 四川大学 | Three-arc harmonic gear hobbing cutter and tooth profile design method thereof |
| CN112059082B (en) * | 2020-09-11 | 2022-08-09 | 汉德车桥(株洲)齿轮有限公司 | Involute spline key tooth modification design method and machining method and gear product thereof |
| CN114799362A (en) * | 2022-06-28 | 2022-07-29 | 湖南中大创远数控装备有限公司 | Grinding machine, bowl-shaped grinding wheel and shape modification method of bowl-shaped grinding wheel |
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